“If you can’t explain it simply, you don’t understand it well enough.” -Albert Einstein

I recently attended a “Mom’s Night Out.” A large group of us decided a few months ago to try and find the best chips and salsa in the area by visiting a restaurant a month. There was much laughter and conversation as we traded mother stories.

Toward the end of the evening one of the moms turned to me and said, “I hear you’re a math guru.” I replied that I may not be a guru, but I’m definitely on a mathematical mission. She went on to explain that she wanted to prepare her children with whatever tools they needed to do well in school. She felt she was doing well with them in reading, but she knew she needed to be doing more in math. Everyone at the table agreed that there’s not a lot out there to help parents with the development of mathematical skills.

I was thrilled to be able to tell them about the focus of my blogs this summer—simple, but effective ways of helping your child understand mathematical concepts. I knew then that today’s blog would begin a series of blogs about my favorite ways to develop number sense with your child.

One way to develop number sense in a preschooler is to use objects that the child uses every day. When my daughter was two we used to have tea parties at her toddler table. We put an animal in every chair. Then we had to give each animal a plate, then a spoon, then a bowl, then a cup. As she went around the table placing each item in front of the animal, we would count up together. We didn’t say the number until the item was placed in front of the animal. Then she would go around the table and count again. She liked moving, placing and counting with real objects for a real purpose. Of course she like pouring the “tea” water into each cup after everyone had their place setting.

This almost daily tea party helped her count up, develop one-to-one correspondence (each animal got each item), and helped her begin to understand relative magnitude (4 represented the number of small spoons and 4 also represented the number of big plates).

What if your child doesn’t like to have tea parties? With my son, who had absolutely NO interest in tea parties, we gave each of his trucks and cars an equal number of riders and tools.

With an older child the partitioning of snacks can be a wonderful opportunity to teach fractions, multiplication, and division. Our children’s grandfather had a giant chocolate bar he gave to them. They decided to divide it between them. They used the “paper-rock-scissors” method of determining who would do the actual division of the bar into equal groups. Our youngest one won. He looked around the table at his two siblings and said he was going to break it in half.

This comment caused a great disturbance in “the force.” His two sisters began to loudly argue that he couldn’t divide the one candy bar in half when there were 3 people eating it. With the same decibel level as his sisters, their brother said, “I won, so I divide it the way I want.”

I hope all parents reading this are laughing. I stepped in after a few minutes, took the bar and gave everyone a chance to reset. After the girls went outside I asked our son to explain why his sisters were upset. I asked him if we could open up the candy bar and see if there was any other way to divide the bar other than by breaking it into half.

When he opened the wrapper he saw the indentions that divided the candy bar into many smaller rectangles. I asked him what he could do to make sure that each person had an equal amount. He got three plates and put each person’s name on the plate. I asked him to count how many rectangles there were in all. He wrote that number on each of the plates.

He spent the next 5 minutes making sure that he gave each plate one chocolate piece at a time until the bar was gone. Thankfully, the number was divisible by 3. If not, you can divide the last piece or pieces into three parts each…another blog will have to explore this concept.

When he finished I asked him to count the number of chocolate rectangles each person had. He wrote that number above the total number of parts. I asked him to hold up his fraction bar (his hand horizontal to the floor) and get his terminator voice ready. In a deep voice, that sounds like the terminator, we pointed to below the line and said, “Denominator, the number of parts in all.”

Then we switched to a high-pitched voice, because the number is on the top, and said, “Numerator, the number of parts you’re talking about.”Each sibling received 6/18 of the chocolate bar. We took the total number of parts and divided them into three equal groups.Our 8th grader was asked to simplify the fraction and then all were allowed to eat.

Are you starting to see the connection between our daily lives and mathematical concepts? Do you see a connection between fractions and the simple sharing into equal groups? In the end, I’m not really sure who made the biggest mess…them eating it or me trying to cut the bar evenly!

In a small-group setting in the classroom the discussions and questions would be the same. I try not to use a lot of food for concrete development of a concept, but graham crackers are easy to divide.

For those of you who want to learn more about developing number sense, here are some more ideas. Crewton Ramone’s House of Math provides pictures and explanations of how children can build walls to understand adding numbers.

http://www.crewtonramoneshouseofmath.com/addends.html

You might want to skim the minilessons authored by Rusty Bresser and Caren Holtzman. These are from their book, Minilessons for Math Practice, Grades K-2. The sample minilesson offers ideas for helping children break apart numbers.

http://www.mathsolutions.com/documents/0-941355-74-8_L.pdf

A page on educationworld.com has an incredible list of games created by Joanne Currah and Jane Felling. You’ll have all the things you need to play these games with your own children and your students if you have dice and playing cards. You may want to take a look at their website for more ideas for your Tabor Rotation Games Station and Manipulative Station. They say they created their company, BOX CARS & ONE-EYED JACKS www.boxcarsandoneeyedjacks.com,  for the sole purpose of making math fun—not threatening or frustrating—for children. They’re my kind of people!

http://www.educationworld.com/a_lesson/archives/boxcars.shtml

As your children and students increase in their ability to think about numbers, you want to encourage them to use mental computation strategies. Origo Education’s website contains articles and examples of how to encourage this type of mathematical thinking.

http://www.origoeducation.com/mental-computation-strategies-addition/

“I hear, I know. I see, I remember. I do, I understand.” -Confucius